A variety of models have been proposed in order to explain Dark Matter (DM), responsible for around a quarter of the total mass-energy density of the Universe [1]}, in terms of scalar particles. The simplest models of this kind invoke an SU(2) singlet [2]}, [3]} or an Inert Doublet Model (IDM) [4]}, [5]}. Other models with additional SU(2) doublets have been proposed and studied. Among the latter, there are some in which the DM stability is provided by a remnant of the symmetry of the potential. Introducing additional SU(2) doublets, see figure REF , in general leads to more flexibility in accommodating dark matter:
